week 7 hw
P1
| Sporting Goods | |||||||||
| (a) | Resource Requirements per Unit | (c-1) | Resource Requirements per Unit | ||||||
| Product | Rubber (lb.) | Leather (ft2) | Product | Rubber (lb.) | Leather (ft2) | ||||
| Basketball | 2.8 | 3.7 | Basketball | 2.8 | 3.7 | ||||
| Football | 1.5 | 5.2 | Football | 1.5 | 5.2 | ||||
| input Constraints | |||||||||
| Total resources available | 600 | 900 | Total resources available | 1000 | 900 | ||||
| Basketball | Football | Basketball | Football | ||||||
| Profits ($) | 11 | 15 | Profits ($) | 11 | 15 | ||||
| Basketball | Decision variables | Basketball | |||||||
| Football | Football | ||||||||
| Maximized profits | Objective function | Maximized profits | |||||||
| (b) | Resource Requirements per Unit | (C-2) | Resource Requirements per Unit | ||||||
| Product | Rubber (lb.) | Leather (ft2) | Product | Rubber (lb.) | Leather (ft2) | ||||
| Basketball | 2.8 | 3.7 | Basketball | 2.8 | 3.7 | ||||
| Football | 1.5 | 5.2 | Football | 1.5 | 5.2 | ||||
| input Constraints | |||||||||
| Total resources available | 600 | 900 | Total resources available | 600 | 1500 | ||||
| Basketball | Football | Basketball | Football | ||||||
| Profits ($) | 12 | 15 | Profits ($) | 11 | 15 | ||||
| Basketball | Decision variables | Basketball | |||||||
| Football | Football | ||||||||
| Maximized profits | Objective function | Maximized profits | |||||||
| Please use computer method to solve the problem | |||||||||
| Please enter your solution in Yellow cells | |||||||||
P2
| A & B products | ||||
| (a) | Hours/ Unit | |||
| Product | Line 1 | Line2 | ||
| A | 11 | 5 | ||
| B | 6 | 9 | ||
| Constraints | ||||
| Total Hours | 65 | 40 | ||
| A | B | |||
| Profits ($) | 11 | 15 | ||
| Product A | decision variables | |||
| Product B | ||||
| Maximized profits | Objective function | |||
| (b) | Sensitivity Range for the coefficient of # of units of product A in the objectivefunction | |||
| Sensitivity Range for the coefficient of # of units of product B in the objectivefunction | ||||
| (c') | Shadow Price for additional hours of production time on Line 1 | |||
| Shadow Price for additional hours of production time on Line 2 | ||||
| Which one of the two the company would prefer (Line 1 or Line 2?) |
P3
| Irwin textile mills | |||||||||
| (a) | Corduroy | denim | |||||||
| Profits for each product | 3.25 | 2.5 | |||||||
| Resources | Available Resources | ||||||||
| Cotton | 8 | 6 | <= | 6500 | |||||
| Labor | 4 | 3 | <= | 3000 | |||||
| Demands | |||||||||
| Corduroy | <= | 510 | |||||||
| denim | <= | 1000000 | |||||||
| Maximized profits | |||||||||
| Write the standard form of the LP model in the space provided below | |||||||||
| (b) | How much extra cotton and processing time are left at the optimal solution? | ||||||||
| Cotton | |||||||||
| Processing Time | |||||||||
| Is the demand for Corduroy met? | |||||||||
| ('c) | If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? | How much? | |||||||
| Processing Time or additional cottone? | |||||||||
| How much? | |||||||||
P4
| Bradley Family | ||||||||
| (a) | Let X1 = # of acres of corn and X2 = # of acres of tobacco | |||||||
| Corn | Tobacco | Resources Available | ||||||
| 300 | 520 | |||||||
| Land | 1 | 1 | <= | 410 | ||||
| Budget | 105 | 210 | <= | 52500 | ||||
| Govt. Restriction | 0 | 1 | <= | 100 | Government Restriction | |||
| X1 | X2 | |||||||
| Decision Variables | ||||||||
| Objective function | ||||||||
| (b) | How many acres of farm land will not be cultivated at the optimal solution? | |||||||
| Do the Bradleys use the entire 100 acre tobacco allotment? | ||||||||
| ('c) | Should the Bradleys' lease extral land from their neighbor at $110 per acre? | |||||||
| What is the maximum price the Bradleys' should pay their neighbor? And how much land shoud they lease? | ||||||||
| maximum price | ||||||||
| # of acres of land | ||||||||
| (d) | For each dollar they borrow , how much additional profit will they make? | |||||||
| If they borrowed a additional $1000, would the number of acres of corn and tobacco they plant change? |